38 Life and Letters of Francis Galton 



namely, that if an individual has h of a certain character, the most prob- 

 able value of the character in his parent will be ^h, and in his grand- 

 parent —^h and his great grandparent — Ji and so on. 

 o o 



Consequently, if we know nothing beyond the one parent of character h, 

 the expected heritage is 



When one grandparent only is known to have h then the corresponding 

 parent has ^h, and the two great grandparents ^h, the four great great 



grandparents — 2 h and so on. Thus the formula is 

 o 



i.e. actually 0"1583&. 



If a parent and the corresponding two grandparents be known Galton 

 says the parent will contribute £ of his character and the two grandparents 

 and their ancestry ^ as above. But I do not think this is correct, even on 

 Galton's assumptions. In the previous case we predicted the great grand- 

 parents and higher ascendants from a knowledge of the grandparents only. 

 But in this case we have not only these two grandparents, but also the 

 knowledge of their offspring, the parent, to predict from, and accordingly 

 Galton's ■g'jj- for the rest of the ancestry is not satisfactory. As he is working 

 in round numbers, Galton puts ^ ( = '075) as equal to '08. 



Three cases are now dealt with : I, both parents only known ; II, four grand- 

 parents only known; and III, both parents and four grandparents known. 

 I gives 2 x "30 = "60 of heritage with a residue of "40 undetermined. Galton 

 distributes this residue in the general population proportions of light to dark 

 eyes after distributing the hazel eyes § to light and ^ to dark eyes, which 

 give 70°/ o and 30% of those eyes. Thus the residue "40 is to be given "28 

 to light and "12 to dark eyes. The corresponding residues for cases II and 

 III are "36 and "18, which Galton distributes as "25 and "11, "12 and "06* 

 respectively. 



Galton now combines all these results in a table from which with know- 

 ledge of the ancestry as far as parents and grandparents are concerned he 

 considers prediction of eye-colour in offspring can be ascertained (p. 39). 



Let me illustrate the use of this table. A family of 12 given by Galton 

 had both parents light-eyed, 3 grandparents light-eyed and 1 hazel-eyed. 

 If we predict from parents only we should have 



12 x (2 x "30 + "28) = 12 x "88 = 10"56 light-eyed. 

 If we predict from grandparents only we should have 



12 x (3 x "16 + 1 x "10 + "25) = 9"96 light-eyed. 



* More accurately the latter pair should be - 13 and -05. 



